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Grades K-5


You re probably familiar with the riddle, "When is a door not a door? When it s ajar." How about this riddle? "When is a cylinder a rectangle?" Give up?

From this lesson your students will find the answer to this riddle and discover the relationship between three-dimensional objects and their two-dimensional building blocks. Students will also view a video segment of an imaginary world where the Flatys feel inferior to the Roundys, leading students to construct familiar three-dimensional objects from their two- dimensional shapes. A final activity will highlight students discoveries of the two- and three- dimensional objects found within the physical and natural world of their school.
ITV Series
Math Works, #5: Exploring Geometric Shapes
Learning Objectives
Students will be able to:
For Teacher--REQUIRED:
SUGGESTED LIST: Select three containers from this list: oatmeal box, butter/margarine box, raisin box, milk carton (any size), brown lunch bag, cereal box, empty bag of potato chips or pretzels

For each student pair:
Whole class access to: crayons, markers, colored pencils, glue, scissors, single hole punch, colored yarn, construction paper

Pre-Viewing Activities
In preparation for the video segment of this lesson, it will be important for you to assess your students understanding of two- and three-dimensional shapes and objects. It will also be important for your students to have a basic understanding that three-dimensional objects are comprised of simple two-dimensional shapes. By taking apart familiar objects such as a paper towel tube, students will begin to see this relationship and relate it to other examples in and out of the classroom.

In order to assess what your students know about two- and three-dimensional shapes and objects and their construction relationship, gather three simple containers from the Suggested Materials list along with the paper towel/toilet paper tube, stick of butter/margarine, paper coffee filter and an orange.

Review with the students the simple geometric shapes of a square, triangle, rectangle and circle by drawing them on the chalkboard and by locating examples of these shapes within your classroom. Explain to your students that these are two-dimensional shapes have only length and height. Identify and label the length and height of each shape.

Next, hold up the paper towel/toilet paper tube and ask: Is this a two-dimensional shape? Students shouldn t recognize it as such, because it is not flat like the simple shapes previously discussed.

Ask: What makes this tube different from a two-dimensional shape like a circle or a square? Students should suggest ideas leading to a description of a three-dimensional object which has length, height, and width (depth). Identify the length, height and width of the tube and also identify the tube as a cylinder.

Ask: What two-dimensional shape will we have if we cut the tube vertically? Listen to the predictions of students, cut the tube vertically and flatten it out. Hold it up and again ask students what two-dimensional shape forms a cylinder. They should respond by saying a rectangle.

On a Container Chart (Appendix A) poster, record your findings. Plan to display the disassembled objects for students to refer to during the lesson.

Then hold up the paper coffee filter. Ask: What two-dimensional shape is used to make this filter? Then hand the filter to a student volunteer and ask her/him to flatten it out on top of a desk. Ask: What did you find out? The student should recognize the flattened filter as a circle.

Repeat this with the stick of wrapped butter/margarine. Ask students to identify and count the two-dimensional shapes that make up the stick (2 squares, 4 rectangles=6 shapes). Next, ask students to predict the two-dimensional shape of the wrapper. Ask for a student volunteer to unwrap the butter/margarine and discuss your findings. Record them on the chart.

Next, hand out the three containers to student volunteers and ask them to take the objects apart in order to reveal their two-dimensional building shapes. Once completed, have the students trace their disassembled container on the chalkboard revealing its actual two-dimensional shapes and then record.
Focus Viewing
To give students a specific responsibility while viewing, ask them to give a thumbs up sign whenever they recognize a three-dimensional object from the Previewing Activity during the video segment. In addition, ask them to be listening for any new classifying or descriptive information about an object which needs to be added to the Comments column on the Container Chart.

Note to Teacher: Prior to viewing, cover the television screen with acetate, plastic wrap or other clear, markable material and have a water soluble or overhead pen ready for use during the video segment. You will also need a spray bottle containing water and paper toweling for cleaning the screen in between pauses.

START video after the opening credits at the Math Works graphic.

PAUSE video on the close up of Jason ( younger boy) lying on the floor with his building blocks after Nancy says . . .so please chill out. Ask: Are these building blocks two or three dimensional? Once students respond three dimensional, RESUME video.

PAUSE video on the close-up of Nancy s blender diagram, after she says, I want to make sure I know how these pieces go back together. Ask: Is a diagram two or three dimensional? Students should respond two dimensional. Ask a student who responds correctly to explain why. Her answer should include the ideas that it s flat and has no depth. RESUME video.

PAUSE video: After Roy (older boy) says to Nancy, Can you hear yourself? A lot of shaping words coming out of your mouth. Ask: What are some of the shaping words Nancy just used? Replay a short segment prior to pausing if the students have a difficult time remembering. The shaping words used by Nancy include square, circular and cylindrical. Ask: What two-dimensional shape does the word circular refer to? Answer: circle. Ask: What two-dimensional shape does cylindrical refer to? Answer: cylinder. RESUME video.

PAUSE video after Nancy says, It s funny, one moment you re seeing something in three dimensions all together and the next. . . Ask: What three-dimensional object is Nancy now seeing in two dimensions? Answer: the blender she s taken apart. RESUME video.

PAUSE video: On the photograph of a fire station ask: What two-dimensional shapes do you see? Trace out each shape with the marking pen as the students identify them. Wipe screen clean. RESUME video.

PAUSE video when Roy says, There s a circular shape on the close-up photo of a child s face. Ask: "What circular shape is Roy referring to? Have the student who correctly identifies the shape come up and trace it with the marking pen. Wipe screen clean. RESUME video.

PAUSE video: After Nancy says, There s a triangular one. . . on a photo of a door. Ask: What two-dimensional object does triangular refer to? Students should respond triangle. RESUME video.

PAUSE video after Nancy says, There s a pyramid on the photo of a building with a pyramidal top. Ask: Where is the pyramid? Have a student volunteer trace out the pyramid on the video screen. Ask the student: What two-dimensional side can we see? Student should answer a triangle. To utilize prediction skills, say: Although we can t see all of the sides, how many triangles do you think make up this pyramid? If the students doesn t guess four ask the class to help out. Even if the students still don t guess four ask: What two-dimensional shape makes up the base of this pyramid? Once students guess a square ask: Now how many triangles make up this pyramid? Students should respond easily now with four. Wipe screen clean. RESUME video.

PAUSE video on the photo of the three smokestacks. As a review of the Previewing Activity, ask: Is this a cylinder? Students should respond yes. Ask: If we cut this cylinder vertically and flattened it out what two-dimensional shape would we have? Students should recognize the comparison with the paper towel/toilet paper tube and respond rectangle. RESUME video.

PAUSE video after host says, Here s a cube. Ask: How many sides does a cube have? Students should respond six. Ask: What two-dimensional shape makes up those six sides? Students should respond squares. RESUME video.

PAUSE video after narrator of cartoon says, . . .where they all loved a flat existence indeed on a close-up of the Flatys yawning. Ask: Are the Flatys two or three dimensional? Students should answer two dimensional and be able to explain why. RESUME video.

PAUSE video after narrator says, They were all real hunks on a close-up of the Roundys. Ask: Are the Roundys two or three dimensional? Why? Students should respond three dimensional with additional information on identifying the object. RESUME video.

PAUSE video after narrator says, If only they could be good, solid citizens instead of being skinny and wimpy. In order to make a prediction, ask: What suggestions would you make to the Flatys about their feelings? Allow students to share their ideas and RESUME video.

PAUSE video after the two circular Flatys say, We could make ourselves into a cylinder. Ask: Do the predictions of these Flatys match any of our observations from the Container Chart? Depending upon the containers you chose, students should be able to recognize the correlation between your class data and the Flatys predictions. RESUME video.

STOP video after the narrator says, Who were really nothing but a lot of flat shapes stuck together when you came to think of it.
At the conclusion of the video segment ask: What did the Flat Earthers learn about themselves that made them realize their similarities to the Round Earthers? Students should answer with ideas about how the Flat Earthers two-dimensional shapes were responsible for the formation of the Round Earthers three-dimensional design.

Refer back to the Previewing Activities and ask: How could we make a diagram of the containers we examined before the video like Nancy did? Students should respond by suggesting to trace around the various sides of the disassembled containers. In order to reinforce lesson objectives ask: Is a diagram two dimensional or three dimensional? Why? Students' answers will lead towards defining the term diagram. Record students ideas about this definition brainstorm style next to the term written on the chalkboard. Repeat this process for the other terms on the chalkboard mentioned as a Focus for Viewing before the video. Ask for two student volunteers to write up a completed version of the definitions as an extra credit assignment. The completed definitions may be written on poster board and then displayed in the classroom.

Next, divide your class into pairs and hand out Shape Up sheets (Appendix B--Worksheets 1a, 1b, 2) to each pair. Depending on your own style, hand out or refer to the additional materials needed to complete this activity (see Materials section--Part One). Explain to the whole class that this activity will give them practice constructing their own Round Earthers from two- dimensional diagrams. Each students pair needs to cut out and construct the three-dimensional objects from Worksheet 1a and 1b and complete the data chart on Worksheet 2 as they work. Students may color and/or decorate the three-dimensional objects as they choose.

Once all of the objects are constructed, have student pairs arrange the objects into a freestanding sculpture on the piece of construction paper. Students will not need to secure the sculpture onto the paper until they complete the next activity. Tell student pairs they are responsible for writing a descriptive paragraph about their sculpture. Encourage students to observe their sculpture from various positions, i.e., rotating it; and points of view, i.e., while standing over it, at eye level, and decide as a pair what perspective they most enjoy. Their paragraph needs to include a name for the sculpture and must describe the sculpture from their favorite perspective. The writing will provide insight into the pairs understanding of the lesson objectives, as well as serve as an excellent opportunity to explore and write from different points of view.

After the sculptures and descriptions are finished, spend some class time allowing pairs to share their projects. Ask: How did you decide on the design of the sculpture? Did you make many changes while designing it? Does your sculpture have a base or did you rely on all of the objects working together? Now, as one student holds up the sculpture, have her/his partner read their description aloud. Ask: How did you name your sculpture? What various arrangements did you try before deciding on one?

As a concluding activity, hold up an orange and say, Nature also provides us with two- and three-dimensional examples. What three-dimensional shape is this? Students need to identify this as a sphere.

Have students make predictions by asking: What two-dimensional shape can make up a sphere? Allow students to respond with their ideas, but do not tell them the correct answer.

Slice the orange in half horizontally and show students the exposed triangular shaped sections. Again ask: Now what two-dimensional shape to you think makes up a sphere? Students should respond triangles. To reinforce this concept, make a slice of orange 1/4 -1/2 thick. Carefully slice through one side of one orange section (Figure 1). Gently pull the slice apart which should separate it into several triangles (Figure 2). Ask: How many triangles do you see? If we continue to cut this orange into slices and separate them like this, can you predict how many triangles would make up this orange? Students predictions will vary.
FIGURE 1 FIGURE 2 cutting line
Continue discussing examples of two and three dimensional objects in nature by asking students to share additional ideas they have. Stimulate discussion by asking: What two-dimensional shapes did the video mention? Can your body make two- or three-dimensional shapes or objects?

PART TWO As a whole class activity, plan to make a tour of your school seeking out the various two- and three-dimensional physical and natural features it has. During the initial tour you take with your students, have them record their own observations of such features in a notebook or by using the suggested data chart from Appendix C. Because you re working towards a tour others will share, emphasize to students the importance of writing their discoveries in the order they observe them.

After the first tour, divide students into groups of 4 or 5 and have each group compile a list of the collected observations composed of their group s favorite six to eight choices. From this listing, make a class list composed of the top choices from all of the groups, probably numbering around 20 depending on your class size. Arrange these points of interest in a logical tour order, consulting your students in the process.

If possible, have a parent volunteer make photos of each point of interest. If not, assign your students to the various points and have them make their own drawings, and then compile a tour portfolio of the photos or drawings. If you are able to make a video, use your students as the tour guides during production.

As you put the portfolio together, hole punch each sheet, use string for the binding and include extra sheets at the end. Then share your tour with another class. Following their tour, perhaps they can add additional discoveries which can be included on the extra sheets.
Once the class s Shapes Tour Portfolio is complete, present it to another class and invite them to take your tour. Perhaps the other class will make their own discoveries and add to the book. Include several blank pages to the end of the portfolio for additional ideas.

If a video tour is created, invite classroom parents in to view it and take the tour for themselves.

Have students create a Shapes Tour of their home (inside or out) or neighborhood.

Have students bring in empty containers from home (perhaps from the Suggested Materials list), disassemble and camouflage them and create a riddle for others to guess what the container was originally used for . Then place their shape riddles and disassembled containers in a school display case for a schoolwide contest. Perhaps a simple prize can be created for correct answers.
Language Arts: Write a follow up episode to the Flat Earth Society cartoon.

Read the Dr. Seuss favorite, The Sneeches, and have students compare and contrast it to the Flat Earth Society cartoon.

Create a class dictionary including definitions for the terms from the video segment and all of the two- and three- dimensional shapes and objects discussed. Encourage students to consider adding any original drawings or diagrams that will enhance their definitions.

Social Studies: As a whole class, view the landscape architect segment of the selected Math Works video. As a class, brainstorm other professions that use geometric shapes and objects as part of their work.

Invite an architect into your class to share and discuss a portfolio of her/his work.

Research into the life of Frank Lloyd Wright. (Access information through CD-Rom programs such as Grolier s Encyclopedia.)

Science: Create Challenge Stations for further research into models and geometric shapes in nature. With a small portion of table salt and sugar and a magnifying glass, students can compare and contrast the two types of crystals. Students should record their findings as well as draw a simple diagram representing the two samples.

Access to other mineral/crystal collections (even pictures from books) for students to examine will reveal naturally occurring geometric shapes. Challenge students to construct models of the crystals they examine using their new knowledge about how three-dimensional objects are formed.

Create a challenge question posing the following predictions, How many one-inch triangles would it take to cover an orange? How many three-inch triangles would it take to cover a basketball?

Music: Select several musical segments for students to listen to which represent a variety of rhythms and textures such as a polka, electronic/synthesized, waltz, rap and classical symphony. Allow students to draw the geometric shapes and objects they hear in the music. Students should share and display these perspectives.

Introduce the students to square-dancing. Point out the various shapes a square dance forms, and ask students to explain how square-dancing received its name.

Encourage students to create a triangle or a circle dance.

Introduce the popular Country Western line dancing.

Master Teacher: Ollire Lane Dunn

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